Charged particle speed detection method based on electrostatic field Fourier transform

Abstract

The invention provides an electrostatic field Fourier transform-based charged particle speed detection method, which is applied to fault monitoring and electrostatic detection of a heavy duty gas turbine, and comprises the following steps: firstly, capturing a time domain electrostatic signal generated by the movement of charged particles falling off due to a fault through an electrostatic field sensor mounted on the inner wall of a gas path pipeline; performing anti-aliasing filtering, amplification and analog-to-digital conversion on the signal to generate a high-fidelity time domain sequence; the method comprises the following steps: extracting a normalized Gaussian pulse signal, performing zero filling to 2N length, and converting the normalized Gaussian pulse signal to a frequency domain by using fast Fourier transform; the 3dB bandwidth of the signal is calculated in the frequency domain, and the particle motion velocity is inversed based on the linear relation obtained through calibration; and finally, the fault type, position and severity are evaluated according to the speed distribution characteristics, the early fault detection of the heavy duty gas turbine is effectively realized, and the method has relatively high reliability and anti-interference capability.

Description

Technical Field

[0001] This invention relates to the field of fault monitoring and electrostatic detection of heavy-duty gas turbines, and in particular to a method for detecting the velocity of charged particles based on the Fourier transform of an electrostatic field. Background Technology

[0002] Heavy-duty gas turbines are large-scale thermodynamic machines that integrate precision aerodynamics, high-temperature materials science, and advanced control technologies. Their core working principle is based on the Brayton cycle, converting the chemical energy of fuel (such as natural gas) into mechanical energy through the continuous operation of three main components: the compressor, combustion chamber, and turbine. They possess outstanding advantages such as high single-unit power, high thermal efficiency, rapid start-up and shutdown, and flexible regulation, and are widely used in core fields such as power generation, petrochemicals, aerospace, and steel, serving as key equipment in modern energy systems.

[0003] Heavy-duty gas turbine systems typically operate in high-temperature, high-pressure environments, where components are subjected to extremely high thermal stress, mechanical stress, and chemical corrosion, making them highly susceptible to gas path failures. Faults in the gas path of heavy-duty gas turbine pipelines can lead to decreased unit output, increased heat rate, and in severe cases, even unplanned shutdowns, resulting in significant economic losses. Therefore, the detection of gas path pipeline failures in heavy-duty gas turbines is crucial for companies to maximize equipment availability and reduce maintenance costs.

[0004] Currently, while traditional detection methods such as performance monitoring and vibration analysis can detect faults in the gas pipelines of heavy-duty gas turbines, significant bottlenecks still exist:

[0005] 1. Limitations of performance monitoring technology

[0006] Performance monitoring methods primarily infer efficiency degradation (such as scaling and corrosion) or flow loss (such as seal wear) by monitoring changes in parameters such as compressor exhaust pressure, exhaust temperature, turbine exhaust temperature, and fuel flow. However, these methods are slow to respond, typically only triggering an alarm after significant performance degradation, and are difficult to pinpoint and identify faults. They are also susceptible to sensor drift and changes in operating conditions.

[0007] 2. Limitations of vibration analysis techniques

[0008] Vibration analysis technology is effective for mechanical faults such as rotor imbalance, misalignment, and bearing wear, but it is not sensitive to early gas path faults such as blade corrosion, coating peeling, and hot channel cracks. It is often only detected when the fault develops to the point of affecting dynamic balance, and lacks early warning capability.

[0009] 3. Current Status of Electrostatic Detection Technology

[0010] Electrostatic detection is an indispensable technical foundation for modern industry to achieve safe production, quality control and process optimization. Through electrostatic field Fourier transform, it can convert the time domain signal related to industrial electrostatic field to the frequency domain, realize the accurate quantification of the performance of electrostatic dissipation materials, trace the source and locate periodic defects in the production process, and effectively separate and filter noise in the monitoring signal. Summary of the Invention

[0011] To address the aforementioned problems, this invention provides a method for detecting the velocity of charged particles based on the electrostatic field Fourier transform, used to monitor abnormal particles in the gas pipeline of a heavy-duty gas turbine, achieving early warning of faults. Specifically, it includes:

[0012] A method for detecting the velocity of charged particles based on electrostatic field Fourier transform, applied to heavy-duty gas turbines, the method comprising:

[0013] S1. Collect the time-domain electrostatic signal of charged particles in the gas pipeline using an electrostatic field sensor;

[0014] S2. Perform anti-aliasing filtering, analog-to-digital conversion, and normalization on the time-domain electrostatic signal of the charged particles to obtain a normalized Gaussian pulse signal;

[0015] S3. Perform zero-filling and fast Fourier transform on the normalized Gaussian pulse signal in sequence to obtain the spectrum data. Calculate the 3dB bandwidth of the corresponding frequency domain signal based on the spectrum data to obtain the frequency domain signal bandwidth.

[0016] S4. Based on the frequency domain signal bandwidth, the approximate linear relationship between the velocity v of the detached particles and the frequency domain signal bandwidth is obtained, and the velocity of the charged particles is obtained.

[0017] Optionally, the anti-aliasing filter in S2 includes:

[0018] An analog low-pass filter is connected between the electrostatic field sensor and the analog-to-digital converter;

[0019] The cutoff frequency of the analog low-pass filter is set to be lower than the Nyquist frequency corresponding to the system sampling frequency.

[0020] Optionally, the analog low-pass filter is a first-order filter or a multi-order filter.

[0021] Optionally, the anti-aliasing filtering and analog-to-digital conversion processing of the time-domain electrostatic signal of the charged particles in step S2 includes:

[0022] After the time-domain electrostatic signal of the charged particles completes anti-aliasing filtering, it is processed by the signal conditioning circuit and then converted from analog to digital to obtain the time-domain signal sequence.

[0023] The signal conditioning circuit is used to amplify and filter the received signal.

[0024] Optionally, the normalization process in S2 includes:

[0025] The time-domain signal sequence is processed using the maximum absolute value normalization method so that all data points are mapped to the interval [-1, 1].

[0026] The image of the normalized Gaussian pulse signal in step S2 is a bell-shaped curve symmetrical about the peak point of the signal intensity.

[0027] Optionally, the zero-padding of the normalized Gaussian pulse signal in S3 includes:

[0028] Add a series (or more) data points with zero values ​​to the end of the normalized Gaussian pulse signal to extend the total length of the normalized Gaussian pulse signal to the power of 2, where N is an integer greater than or equal to 10.

[0029] Optionally, the Fast Fourier Transform in S3 includes:

[0030] Apply a Hanning window to the zero-filled normalized Gaussian pulse signal and then perform a fast Fourier transform.

[0031] Zero padding is performed during the Fast Fourier Transform process.

[0032] After the fast Fourier transform is completed, the one-sided spectrum is calculated, peak normalization is performed, and the logarithm of the frequency axis is taken to obtain the spectrum data.

[0033] The frequency range is set to 0 to fs / 2 Hz, where fs is the sampling frequency.

[0034] Optionally, the approximately linear relationship between the detached particle velocity v and the frequency domain signal bandwidth in S4 is: v = k·BW + b;

[0035] Where k and b are values ​​obtained through linear regression analysis, v is the velocity of the detached particles, and BW is the bandwidth of the frequency domain signal.

[0036] The above technical solution has at least the following advantages compared with the existing technology:

[0037] Traditional electrostatic detection technologies can mostly only qualitatively determine whether particles have detached from the gas path, or roughly estimate particle size through signal energy, and cannot obtain dynamic information about particle motion. This invention, through frequency domain feature extraction and linear inversion algorithms, achieves for the first time a precise quantitative measurement of the velocity of detached particles, elevating fault detection from a vague qualitative level to a precise quantitative diagnostic level.

[0038] This invention extracts the 3dB bandwidth corresponding to the main peak frequency where energy is most concentrated in the spectrum. This is a very significant and stable feature, with a signal-to-noise ratio far higher than other parts of the signal. This makes the fault diagnosis logic clear and explicit. Compared to traditional techniques that rely on complex time-domain waveforms or the energy integral of the entire signal, this invention has a strong ability to suppress environmental noise and electromagnetic interference, making it particularly suitable for the harsh operating conditions of heavy-duty gas turbines under high temperature and high pressure.

[0039] Traditional detection technologies typically only issue warnings when a component has already experienced measurable performance degradation or obvious damage, resulting in late alerts. This invention, by detecting the presence and velocity changes of tiny detached particles, can issue warnings at the nascent stage of a fault, buying valuable time for maintenance decisions. For example, when an abnormal change in particle velocity distribution is detected, it can be determined that a specific component may be experiencing early wear.

[0040] Traditional technologies can only roughly determine equipment degradation trends by monitoring the frequency of debris events, resulting in limited predictive capabilities due to their single data dimension. This invention not only monitors the frequency of particle shedding but, more importantly, tracks the distribution and evolution of particle velocity over a long period. This quantitative data, encompassing dynamic trends, is crucial for accurate predictive maintenance, helping companies to schedule repairs before failures occur, maximizing equipment availability and reducing maintenance costs. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A complete implementation flowchart of a method for detecting the velocity of charged particles in the gas path of a heavy-duty gas turbine based on electrostatic field Fourier transform is provided in this embodiment of the invention.

[0043] Figure 2 This is a schematic diagram of the system composition provided in an embodiment of the present invention;

[0044] Figure 3 This is a flowchart illustrating the data processing steps involved in the entire process from the acquisition of time-domain electrical signals generated by detached particles to the FFT, as provided in an embodiment of the present invention.

[0045] Figure 4The present invention provides a time-domain potential signal corresponding to the particles falling off the gas pipeline of a heavy gas turbine at different speeds, obtained by finite element simulation analysis using COMSOL Multiphysics and collected by an electrostatic field sensor.

[0046] Figure 5 Provided for embodiments of the present invention Figure 4 The time-domain normalized Gaussian pulse signal corresponding to the time-domain potential signal of particles falling off at different speeds;

[0047] Figure 6 The embodiments of the present invention provide a basis for... Figure 5 The spectrum obtained by performing FFT on the time-domain normalized Gaussian pulse signal corresponding to the time-domain potential signal of particles falling at different speeds;

[0048] Figure 7 The embodiments of the present invention provide a basis for... Figure 5 A schematic diagram showing the linear fit between the time-domain potential signal of particles falling at different velocities and their velocity in the frequency domain. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0050] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms “first,” “second,” and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an,” “a,” or “the,” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising,” “including,” or “including,” and similar terms mean that the element or object preceding the word encompasses the element or object listed following the word and its equivalents, without excluding other elements or objects. The terms “connected,” “linked,” or “connected,” and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0051] To address the shortcomings of electric field Fourier transform in early fault detection of gas pipelines in heavy-duty gas turbines, this invention provides a method for detecting the velocity of charged particles based on electrostatic field Fourier transform. The method involves performing a Fourier transform on the time-domain potential signal generated by detached particles when a fault occurs in the gas pipeline of a heavy-duty gas turbine, collected by an electrostatic field sensor. The characteristics of the frequency domain signal are extracted, and spectral analysis is performed to obtain the velocity of the detached particles. By detecting the appearance and velocity changes of detached particles, an early warning can be issued at the initial stage of a fault in the gas pipeline of a heavy-duty gas turbine.

[0052] Specifically, it includes the following:

[0053] like Figures 1 to 7 As shown, a method for detecting the velocity of charged particles based on electrostatic field Fourier transform is applied to heavy-duty gas turbines. The method includes:

[0054] S1. Collect the time-domain electrostatic signal of charged particles in the gas pipeline using an electrostatic field sensor;

[0055] S2. Perform anti-aliasing filtering, analog-to-digital conversion, and normalization on the time-domain electrostatic signal of the charged particles to obtain a normalized Gaussian pulse signal;

[0056] S3. Perform zero-filling and fast Fourier transform on the normalized Gaussian pulse signal in sequence to obtain the spectrum data. Calculate the 3dB bandwidth of the corresponding frequency domain signal based on the spectrum data to obtain the frequency domain signal bandwidth.

[0057] S4. Based on the frequency domain signal bandwidth, the approximate linear relationship between the velocity v of the detached particles and the frequency domain signal bandwidth is obtained, and the velocity of the charged particles is obtained.

[0058] In one specific implementation, S1, the time-domain electrostatic signal of charged particles in the gas pipeline is collected by an electrostatic field sensor, specifically including:

[0059] The present invention first installs an electrostatic field sensor on the inner wall of the gas pipeline of a heavy-duty gas turbine. When the gas pipeline of the heavy-duty gas turbine malfunctions, the falling particles generate an electrical signal due to their charge. The sensor collects the electrical signal when the falling particles move through the airflow.

[0060] In one specific implementation, S2, the time-domain electrostatic signal of the charged particle is subjected to anti-aliasing filtering, analog-to-digital conversion, and normalization processing to obtain a normalized Gaussian pulse signal, specifically including:

[0061] ① Anti-aliasing filtering:

[0062] An analog low-pass filter is connected between the electrostatic field sensor and the analog-to-digital converter; the analog low-pass filter is a first-order filter or a multi-order filter. The cutoff frequency of the analog low-pass filter is set to be lower than the Nyquist frequency corresponding to the system sampling frequency.

[0063] The principle is as follows: When using an electrostatic field sensor to collect the time-domain potential signal caused by charged detached particles generated due to a fault in the gas pipeline of a heavy-duty gas turbine, anti-aliasing filtering measures are needed to prevent high-frequency components in the signal above the Nyquist frequency (i.e., half the sampling frequency) from aliasing during the sampling process and folding into the frequency band below the Nyquist frequency, thus causing severe spectrum distortion. Specifically, this measure involves connecting a first-order or multi-order analog low-pass filter between the electrostatic field sensor and the analog-to-digital converter (ADC), with its cutoff frequency strictly set below the Nyquist frequency corresponding to the current sampling frequency of the system. This effectively suppresses high-frequency interference components above this cutoff frequency, ensuring sufficient attenuation before entering the sampling system and guaranteeing the accuracy and reliability of subsequent signal processing.

[0064] ② Analog-to-digital conversion:

[0065] After the time-domain electrostatic signal of the charged particles completes anti-aliasing filtering, it is processed by the signal conditioning circuit and then converted from analog to digital to obtain a time-domain signal sequence. The signal conditioning circuit is used to amplify and filter the received signal to obtain a high-fidelity time-domain signal sequence.

[0066] ③ Normalization processing includes:

[0067] The time-domain signal sequence is processed using the maximum absolute value normalization method so that all data points are mapped to the interval [-1, 1]. The image of the normalized Gaussian pulse signal is a bell-shaped curve symmetrical about the peak point of the signal intensity.

[0068] The specific principle involves extracting a pulse signal from the time-domain potential signal acquired by an electrostatic field sensor and performing maximum absolute value normalization on it. To implement the above pulse signal processing operations, the required functions are all called from Python libraries.

[0069] The specific process is as follows:

[0070] First, the absolute values ​​of each data point of the original signal are taken using the numpy.abs() function, and the precise location of the signal peak is located using numpy.argmax(), which is then used as the pulse time center point.

[0071] Subsequently, the round() function is used to calculate the number of samples within a 0.5-second time window before and after the center point, and numpy.zeros() is used to generate an array of a specified length with all zeros to store the truncated pulse signal.

[0072] Next, the max() and min() functions are used to ensure that the calculated cutoff boundary does not exceed the actual index range of the original data, and array slicing operations are used to extract the data of the corresponding segments from the original signal and fill them into the pre-created zero-padding array.

[0073] Finally, the numpy.max() and numpy.abs() functions are called again to find the maximum absolute value in the pulse data segment. The entire pulse signal data is then divided by this maximum value using array division, thereby achieving normalization.

[0074] In one specific implementation, S3, the normalized Gaussian pulse signal is sequentially subjected to zero-filling and fast Fourier transform to obtain spectral data. Based on the spectral data, the 3dB bandwidth of the corresponding frequency domain signal is calculated to obtain the frequency domain signal bandwidth, specifically including:

[0075] Add a series (or more) data points with zero values ​​to the end of the normalized Gaussian pulse signal to extend the total length of the normalized Gaussian pulse signal to the power of 2, where N is an integer greater than or equal to 10.

[0076] The total length of the Gaussian pulse signal here refers to the number of Gaussian pulse signals.

[0077] Apply a Hanning window to the zero-filled normalized Gaussian pulse signal and then perform a fast Fourier transform.

[0078] Zero padding is performed during the Fast Fourier Transform process.

[0079] After the fast Fourier transform is completed, the one-sided spectrum is calculated, peak normalization is performed, and the logarithm of the frequency axis is taken to obtain the spectrum data.

[0080] The frequency range is set to 0 to fs / 2 Hz, where fs is the sampling frequency.

[0081] The specific principle involves the following: Before performing FFT analysis on the time-domain potential signal of charged detached particles generated by a fault in the gas pipeline of a heavy-duty gas turbine, collected by an electrostatic field sensor, zero-padding and frequency domain interpolation operations are performed on the signal to improve spectral resolution and make the transformed spectrum lines denser and smoother. The specific implementation of this operation is as follows: a series of zero-valued data points are added to the end of the original time-domain signal, extending the total length of the signal to 218 bits. This reduces the frequency interval between adjacent frequency points in the spectrum, increases the number of frequency points in the spectrum, and calculates the amplitude corresponding to the added frequency points based on the FFT algorithm for frequency domain interpolation. This significantly improves the detail and continuity of the spectrum display without changing the original signal's physical characteristics, providing a more reliable basis for subsequent frequency domain feature extraction and fault diagnosis.

[0082] In one specific implementation method, S4, based on the frequency domain signal bandwidth, an approximately linear relationship is obtained between the velocity v of the detached particles and the frequency domain signal bandwidth, thus obtaining the velocity of the charged particles:

[0083] The approximate linear relationship between the velocity v of the detached particles and the bandwidth of the frequency domain signal is: v = k·BW + b;

[0084] Where k and b are values ​​obtained through linear regression analysis, v is the velocity of the detached particles, BW is the bandwidth of the frequency domain signal, and k and b are pre-calibrated experimentally.

[0085] In practical use, this method can be used to perform correlation analysis on the type, size, detachment location, and wear degree of the gas turbine based on the velocity and velocity distribution of the detached particles, or, combined with the experience of those skilled in the art, to conduct a preliminary assessment of the faults and fault degrees of the gas pipelines of heavy-duty gas turbines.

[0086] The specific principle of this invention is as follows: On a PC, an FFT is performed on the preprocessed normalized Gaussian pulse signal. Then, the logarithm of the frequency axis of the resulting spectrum is taken to obtain the logarithmic frequency amplitude diagram of the signal. Finally, its bandwidth (BW) is calculated in the frequency domain. , and by Figure 5 It can be seen that the faster the speed, the narrower the pulse; the slower the speed, the wider the pulse. Therefore Therefore, the relationship between the velocity of detached particles generated during a fault in the gas pipeline of a heavy-duty gas turbine and the BW relationship of the particle's electrical signal in the frequency domain can be described as follows: ( (Pre-calibrated by the experiment), by Figure 7 It can be known Therefore, the velocity of the electrical signal generated by the detached particles can be inverted in the frequency domain by calculating the BW of the electrical signal, and the fault and its degree can be detected in the gas pipeline of heavy gas turbines based on its velocity distribution.

[0087] Traditional electrostatic detection technologies can mostly only qualitatively determine whether particles have detached from the gas path, or roughly estimate particle size through signal energy, and cannot obtain dynamic information about particle motion. This invention, through frequency domain feature extraction and linear inversion algorithms, achieves for the first time a precise quantitative measurement of the velocity of detached particles, elevating fault detection from a vague qualitative level to a precise quantitative diagnostic level.

[0088] This invention extracts the 3dB bandwidth corresponding to the main peak frequency where energy is most concentrated in the spectrum. This is a very significant and stable feature, with a signal-to-noise ratio far higher than other parts of the signal. This makes the fault diagnosis logic clear and explicit. Compared to traditional techniques that rely on complex time-domain waveforms or the energy integral of the entire signal, this invention has a strong ability to suppress environmental noise and electromagnetic interference, making it particularly suitable for the harsh operating conditions of heavy-duty gas turbines under high temperature and high pressure.

[0089] Traditional detection technologies typically only issue warnings when a component has already experienced measurable performance degradation or obvious damage, resulting in late alerts. This invention, by detecting the presence and velocity changes of tiny detached particles, can issue warnings at the nascent stage of a fault, buying valuable time for maintenance decisions. For example, when an abnormal change in particle velocity distribution is detected, it can be determined that a specific component may be experiencing early wear.

[0090] The following points need to be explained:

[0091] (1) The accompanying drawings of the embodiments of the present invention only involve the structures involved in the embodiments of the present invention. Other structures can refer to the general design.

[0092] (2) For clarity, the thickness of layers or regions is enlarged or reduced in the drawings used to describe embodiments of the invention, i.e., these drawings are not drawn to scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being “above” or “below” another element, the element may be “directly” located “above” or “below” the other element or there may be intermediate elements.

[0093] (3) Where there is no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0094] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for detecting the velocity of charged particles based on electrostatic field Fourier transform, characterized in that, Applied to heavy-duty gas turbines, the method includes: S1. Collect the time-domain electrostatic signal of charged particles in the gas pipeline using an electrostatic field sensor; S2. Perform anti-aliasing filtering, analog-to-digital conversion, and normalization on the time-domain electrostatic signal of the charged particles to obtain a normalized Gaussian pulse signal; S3. Perform zero-filling and fast Fourier transform on the normalized Gaussian pulse signal in sequence to obtain the spectrum data. Calculate the 3dB bandwidth of the corresponding frequency domain signal based on the spectrum data to obtain the frequency domain signal bandwidth. S4. Based on the frequency domain signal bandwidth, the approximate linear relationship between the velocity v of the detached particles and the frequency domain signal bandwidth is obtained, and the velocity of the charged particles is obtained.

2. The method for detecting the velocity of charged particles based on electrostatic field Fourier transform according to claim 1, characterized in that, The anti-aliasing filter in S2 includes: An analog low-pass filter is connected between the electrostatic field sensor and the analog-to-digital converter; The cutoff frequency of the analog low-pass filter is set to be lower than the Nyquist frequency corresponding to the system sampling frequency; The system sampling frequency is 22Hz.

3. The method for detecting the velocity of charged particles based on electrostatic field Fourier transform according to claim 2, characterized in that, The analog low-pass filter is a first-order filter or a multi-order filter.

4. The method for detecting the velocity of charged particles based on electrostatic field Fourier transform according to claim 3, characterized in that, The anti-aliasing filtering and analog-to-digital conversion processing of the time-domain electrostatic signal of the charged particles in step S2 includes: After the time-domain electrostatic signal of the charged particles completes anti-aliasing filtering, it is processed by the signal conditioning circuit and then converted from analog to digital to obtain the time-domain signal sequence. The signal conditioning circuit is used to amplify and filter the received signal.

5. The method for detecting the velocity of charged particles based on electrostatic field Fourier transform according to claim 4, characterized in that, The normalization process in S2 includes: The time-domain signal sequence is processed using the maximum absolute value normalization method so that all data points are mapped to the interval [-1, 1]. The image of the normalized Gaussian pulse signal in step S2 is a bell-shaped curve symmetrical about the peak point of the signal intensity.

6. The method for detecting the velocity of charged particles based on electrostatic field Fourier transform according to claim 5, characterized in that, The zero-padding of the normalized Gaussian pulse signal in S3 includes: Multiple data points with zero values ​​are added to the end of the normalized Gaussian pulse signal to extend the total length of the normalized Gaussian pulse signal to a power of 2, where N is an integer greater than or equal to 10.

7. The method for detecting the velocity of charged particles based on electrostatic field Fourier transform according to claim 6, characterized in that, The Fast Fourier Transform in S3 includes: Apply a Hanning window to the zero-filled normalized Gaussian pulse signal and then perform a fast Fourier transform. Zero padding is performed during the Fast Fourier Transform process. After the fast Fourier transform is completed, the one-sided spectrum is calculated, peak normalization is performed, and the logarithm of the frequency axis is taken to obtain the spectrum data. The frequency range is set to 0 to fs / 2 Hz, where fs is the sampling frequency.

8. The method for detecting the velocity of charged particles based on electrostatic field Fourier transform according to claim 6, characterized in that, The approximate linear relationship between the detached particle velocity v in S4 and the frequency domain signal bandwidth is: v = k·BW + b; Where k and b are values ​​obtained through linear regression analysis, v is the velocity of the detached particles, and BW is the bandwidth of the frequency domain signal.

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